Without loss, assume that \(A\ne 0\) . Consider the set \(\mathrm {Reg}(A)\subseteq A\)  consisting of all non-singular points of \(A\) –these are the points where the dimension of the Zariski tangent space to \(A\)  is exactly equal to \(\dim (A)\) . It is well-known [1]} that \(\mathrm {Sing}(A)=A\setminus \mathrm {Reg}(A)\)  is an algebraic subset of \(A\)  of dimension strictly smaller than \(\dim (A)\) ; in particular, \(\mathrm {Reg}(A)\ne 0\)  and \(\mathrm {Reg}(A)\)  is a relatively open subset of \(A\) .
